91影视

Sleep deprivation Does sleep deprivation linger for more than a day? Researchers designed a study using 21 volunteer subjects between the ages of 18 and 25. All 21 participants took a computer-based visual discrimination test at the start of the study. Then the subjects were randomly assigned into two groups. The 11 subjects in one group, D, were deprived of sleep for an entire night in a laboratory setting. The 10 subjects in the other group, A, were allowed unrestricted sleep for the night. Both groups were allowed as much sleep as they wanted for the next two nights. On Day 4, all the subjects took the same visual discrimination test on the computer. Researchers recorded the improvement in time (measured in milliseconds) from Day 1 to Day 4 on the test for each subject.\(^{41}\) We used Fathom software to randomly reassign the 21 subjects to the two groups 1000 times, assuming the treatment received doesn鈥檛 affect each individual鈥檚 time improvement on the test. The dotplot shows the approximate randomization distribution of \(\overline{x}_{\mathrm{A}}-\overline{x}_{\mathrm{D}}\). (a) Explain why the researchers didn鈥檛 let the subjects choose whether to be in the sleep deprivation group or the unrestricted sleep group. (b) In the actual experiment, \(\overline{x}_{\mathrm{A}}-\overline{x}_{\mathrm{D}}=15.92 .\) This value is marked with a blue line in the figure. What conclusion would you draw? Justify your answer with appropriate evidence. (c) Based on your conclusion in part (b), could you have made a Type I error or a Type II error? Justify your answer.

Step by step solution

01

Understanding Random Assignment

Researchers didn't allow the subjects to choose their groups to reduce bias. Random assignment helps ensure that any differences observed between the two groups (sleep deprived and unrestricted sleep) are due to the effects of the sleep condition, not pre-existing differences among subjects.

02

Analyzing the Dotplot Result

The value \(\overline{x}_{\mathrm{A}}-\overline{x}_{\mathrm{D}} = 15.92\) lies on the right end of the randomization distribution, indicating that the observed difference is much larger than expected by random chance. This suggests that sleep deprivation might have an effect on the improvement times in the test.

03

Drawing a Conclusion

Since the observed difference of 15.92 is significant in comparison to the random distribution, we can conclude that there is an effect of sleep deprivation on the visual discrimination test improvement time. There is strong evidence to reject the null hypothesis that sleep condition does not affect the performance improvement.

04

Considering Type I and Type II Errors

A Type I error occurs if we wrongly reject a true null hypothesis. Given our conclusion from part (b), there is a risk of committing a Type I error if the null hypothesis is actually true. Alternatively, a Type II error would occur if we failed to detect a real effect of sleep deprivation, which doesn't apply in our conclusion as we have found evidence of an effect.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Random Assignment

In experiments like the sleep deprivation study you've encountered, random assignment plays a crucial role. The key idea is to reduce or eliminate bias in how subjects are placed into different groups.
Imagine if participants could choose their own group. Those who feel they can handle sleep deprivation might opt for that group, while others who enjoy sleep may choose the unrestricted rest group. This voluntary selection introduces bias.

With random assignment, each subject has an equal chance of being placed in any group. It ensures that the differences observed in the outcomes between groups are likely due to the treatment (in this case, sleep deprivation), and not because of any pre-existing differences between the participants.

• By randomizing, researchers increase the reliability of their results.
• It helps in providing stronger evidence of causality by balancing unknown and known factors across different test groups.

Hence, in the study you reviewed, using random assignment helps to make a fair comparison between the sleep-deprived participants and those with unrestricted sleep.

Type I and Type II Errors

When evaluating the results of an experiment, like in the sleep deprivation study, it's essential to understand potential errors that could affect conclusions. These errors are known as Type I and Type II errors.
**Type I Error** occurs when we reject a true null hypothesis. It's like thinking there's an effect of sleep deprivation when there isn't any. In other words, believing there's a difference between groups caused by the treatment when it's actually due to random variation.

• In the study, we concluded that sleep deprivation affects test performance. If this conclusion is incorrect when the truth is there's no effect, you'd have made a Type I error.

**Type II Error**, on the other hand, happens when we fail to reject a false null hypothesis. Here, we'd mistakenly see no effect of sleep deprivation when it actually matters.

• This type of error would occur if the results showed no difference in test scores, while in reality, sleep deprivation did impact the performance significantly.

Understanding these errors helps in assessing the reliability of the research findings and in making more accurate conclusions.

Null Hypothesis Testing

Null hypothesis testing is a statistical method used to determine if there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. In your sleep deprivation study, the null hypothesis was that sleep condition (sleep deprivation or unrestricted sleep) does not affect the improvement in visual discrimination test scores.
Researchers attempt to find out whether the observed results, like the 15.92 difference in test improvement score, could occur by random chance. If the results are too extreme or rare under the null hypothesis, it's usually rejected.

• In your example, the dotplot showed the randomization distribution of the test score differences. The fact that the observed value of 15.92 was far from the center of this distribution suggests it's unlikely to occur if the null hypothesis were true.
• This provides evidence to support the alternative hypothesis, which is that sleep deprivation does indeed have an effect on the test scores.

Through null hypothesis testing, researchers can make well-supported decisions about their research questions, helping to confirm if their alternative hypothesis holds or if they should continue to hold onto the null assumption.